Entangling dynamics from effective rotor/spin-wave separation in U(1)-symmetric quantum spin models

Abstract

The non-equilibrium dynamics of quantum spin models is a most challenging topic, due to the exponentiality of Hilbert space; and it is central to the understanding of the many-body entangled states that can be generated by state-of-the-art quantum simulators. A particularly important class of evolutions is the one governed by U(1) symmetric Hamiltonians, initialized in a state which breaks the U(1) symmetry -- the paradigmatic example being the evolution of the so-called one-axis-twisting (OAT) model, featuring infinite-range interactions between spins. In this work we show that the dynamics of the OAT model can be closely reproduced by systems with power-law-decaying interactions, thanks to an effective separation between the zero-momentum degrees of freedom, associated with the so-called Anderson tower of states, and reconstructing a OAT model; and finite-momentum ones, associated with spin-wave excitations. This mechanism explains quantitatively the recent numerical observation of spin squeezing and Schrödinger-cat generation in the dynamics of dipolar Hamiltonians; and it paves the way for the extension of this observation to a much larger class of models of immediate relevance for quantum simulations.

arXiv comment5+3 pages, 3+2 figures

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Cited by in corpus (8)

• Scalable spin squeezing in a dipolar Rydberg atom array
• Quantum-enhanced sensing on an optical transition via emergent collective quantum correlations
• Spectroscopy of elementary excitations from quench dynamics in a dipolar XY Rydberg simulator
• Magnetism in the two-dimensional dipolar XY model
• Theory of robust quantum many-body scars in long-range interacting systems
• Rotor/spin-wave theory for quantum spin models with U(1) symmetry
• Fast and Accurate Greenberger-Horne-Zeilinger Encoding Using All-to-all Interactions
• Nonequilibrium Critical Scaling of a Squeezing Phase Transition